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Zbl 0863.34022
Agarwal, Ravi P.; O'Regan, Donal
Singular boundary value problems for superlinear second order ordinary and delay differential equations. (English)
[J] J. Differ. Equations 130, No.2, 333-355 (1996). ISSN 0022-0396

The authors study the existence of solutions for the following singular boundary value problems for nonlinear second order ordinary and delay differential equations: $$\cases y''(t)+ q(t)f(t,y(t))=0, &0<t<1,\\ y(0)= y(1)=0;\endcases \tag 1$$ $$\cases {1\over{p(t)}} (p(t)y'(t))'+ q(t)f(t,y(t))=0, &0<t<1,\\ {\displaystyle {\lim_{t\searrow 0}}} p(t)y'(t)= y(1)=0;\endcases \tag 2$$ $$\cases y''(t)+ q(t)f(t,y(t-r))=0, &t\in(0;1) \setminus\{r\},\\ y(t)= \mu(t), &t\in[-r;0],\\y(1)=0, &0<r<1,\ r=\text{const}.\endcases \tag 3$${}.
[T.-D.Havarneanu (Iaşi)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34K10 Boundary value problems for functional-differential equations

Keywords: singular boundary value problem; second order differential equations; delay differential equations

Cited in: Zbl 1104.34012

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